Modified closed-form solutions for three-dimensional elastic deformations of a composite structure containing macro-scale spherical gas/liquid inclusions

摘要

We re-examine the three-dimensional linearly elastic deformations of a composite structure consisting of an infinite isotropic elastic matrix into which is embedded a macro-sized spherical compressible gas/liquid inclusion. Our main focus lies on the contribution resulting from changes in the initial pressure inside the inclusion during deformation. In this respect, we include not only the effect of the change in pressure induced by the change in volume of the inclusion during deformation but also by the variation of the direction of the pressure with the direction of the normal to the deforming inclusion-matrix interface; this latter contribution has been largely neglected in the majority of studies in this area. In doing so, we incorporate a more complete description of the influence of the initial pressure inside the inclusion on the elastic response of the composite structure when certain external loadings are applied to the matrix. In particular, we obtain an analytical representation for the full displacement field in the matrix in the case of a uniform far-field uni-axial loading and, using effective medium theories, we also derive explicit expressions for the effective properties of the composite structure and illustrate the influence of changes in the initial pressure using numerical examples.